Dear Chen-Gia Tsai,
Once more you provided evidence for what is at least my guess but perhaps
your finding: Pitch apparently relates to a kind of autocorrelation that is
not based on phase locking but presumably on a joint mechanism according to
Wiener-Chintchine theorem. It includes a neural second analysis of a
preceding cochlear Cosine transform followed by one-way rectification. Such
envisioned joined main mechanism of hearing would largely correspond to
real valued cepstral analysis. In VDI Fortschrittsberichte Nr.579, Wolfgang
Riedißer clarified, the complex cepstrum of a real causal signal is real.
In other words, hearing can be understood without complex calculus. After
18 months of tenacious discussion, a theoretical physicist eventually
admitted that my suggested use of real-valued Fourier cosine transform is
mathematically correct and apologized for his distrust. Meanwhile I dealt
with a modification of FCT in order to better allow for CB. Hopefully, work
by those who dealt with the role of multipolars within CN will further
elucidate what happens. I already reminded of Gerald Langner and will add
Lutz Wiegrebe. Are musical scale and chords based on something like
cepstrum rather than frequency? Why not?
Kind regards,
Eckard
pitches appear somewhat ambiguous. The frequency difference of adjacent
components is 800 Hz in these complex tones. As they do not have the same
pitch of 800 Hz, the pitch could not be extracted in terms of the temporal
envelop of adjacent components.
>
>Pitch models based on autocorrelation analysis or coincidence detection
(Shamma and Klein: The case of the missing pitch templates: How harmonic
templates emerge in the early auditory system. JASA 107:2631-44) could
explain the multi-pitch effect of tones composed of upper odd-numbered
harmonics, if temporal cues for pitch extraction were assumed to be
maintained in the range of 4 - 6 kHz.
>This finding prompts the question: is there considerable phase locking up
to 6 kHz?
>
>For more audio files demonstrating the multi-pitch effect of tones
composed of upper odd-numbered harmonics, see
>http://www.yogimont.net/jia/nasality_hollowness/multi-pitch.html
>
>
>Any comment is much appreciated.
>
>Best,
>Chen-Gia Tsai
>
>______________________________________
>Chen-Gia Tsai
>Ph.D Musicology, Humboldt University Berlin
>http://www.yogimont.net/jia/
>tsai.cc@lycos.com
>
>
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